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Modular Structures as Dependent Types in Isabelle [chapter]

Florian Kammüller
1999 Lecture Notes in Computer Science  
Hence, they enable adequate formalization of abstract algebraic structures and a natural proof style.  ...  Dependent types, constructed as HOL sets, are used to represent modular structures by semantical embedding. The modules remain rst class citizen of the logic.  ...  The class of all groups is represented by a HOL set over this record type. This paper rst explains our notion of algebraic structures and gives examples in Sect. 2.  ... 
doi:10.1007/3-540-48167-2_9 fatcat:gr7gyglb2jbpjgg75yhdcvxesi

On the structure of L-algebra L(Cvir)

Denis Juriev
1991 Journal of Functional Analysis  
The scenery of the theory of groups, their representations, and homogeneous spaces in view of the intensive interaction with the mathematical physics deeply depends on changes in it.  ...  the theory of representations of the infinite dimensional algebras and groups.  ...  To find the integral formula for the transformation R,R;' from the direct recording to the reversed recording in the L-algebra L( Ccir). ACKNOWLEDGMENTS  ... 
doi:10.1016/0022-1236(91)90143-s fatcat:mxkstf5z6jcunijn4iikyeiwnu

Packaging Mathematical Structures [chapter]

François Garillot, Georges Gonthier, Assia Mahboubi, Laurence Rideau
2009 Lecture Notes in Computer Science  
This paper proposes generic design patterns to define and combine algebraic structures, using dependent records, coercions and type inference, inside the Coq system.  ...  Our methodology is robust enough to handle a hierarchy comprising a broad variety of algebraic structures, from types with a choice operator to algebraically closed fields.  ...  Specifically, we have found that well-known encodings of algebraic structures using dependent types and records [2] break down in the face of complexity; we address this issue in section 2 of this paper  ... 
doi:10.1007/978-3-642-03359-9_23 fatcat:vkan4oitzberffz5sd6b3ukkju

Extensible language implementation with object algebras (short paper)

Maria Gouseti, Chiel Peters, Tijs van der Storm
2014 SIGPLAN notices  
This experience has led to a simple, yet powerful set of tools for the practical and flexible implementation of highly extensible languages.  ...  Object Algebras are a recently introduced design pattern to make the implementation of recursive data types more extensible.  ...  Calling factory methods on this algebra will create a structure that can recreate the same structure into another algebra.  ... 
doi:10.1145/2775053.2658765 fatcat:pdcfcpqdfbcqba2kn2ih6jk42y

Extensible language implementation with object algebras (short paper)

Maria Gouseti, Chiel Peters, Tijs van der Storm
2014 Proceedings of the 2014 International Conference on Generative Programming: Concepts and Experiences - GPCE 2014  
This experience has led to a simple, yet powerful set of tools for the practical and flexible implementation of highly extensible languages.  ...  Object Algebras are a recently introduced design pattern to make the implementation of recursive data types more extensible.  ...  Calling factory methods on this algebra will create a structure that can recreate the same structure into another algebra.  ... 
doi:10.1145/2658761.2658765 dblp:conf/gpce/GousetiPS14 fatcat:55g2buypuzdudob4w7czostv6u

Leveraging the Information Contained in Theory Presentations [article]

Jacques Carette, William M. Farmer, Yasmine Sharoda
2020 arXiv   pre-print
Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of which was started as Universal Algebra.  ...  Various constructions (homomorphism, term algebras, products, etc) and their properties are both universal and constructive. Thus they are ripe for being automated.  ...  We envision a framework in which the contents of the library can be defined succinctly, and elaborated to a large reusable and flexible body of standardized mathematics knowledge.  ... 
arXiv:2006.09292v1 fatcat:rv4mfzpxwbdnlnqatxbuvgoxoq

Page 4453 of Mathematical Reviews Vol. , Issue 82j [page]

1982 Mathematical Reviews  
“This paper surveys the history of data structures used for tables, files or record management systems: structures designed for efficient retrieval, insertion and deletion of single records characterized  ...  A naive approach would be to complete F* , the set of functional dependencies that are implied by F, project F* onto the database scheme, and determine whether the resulting set of dependencies covers  ... 

A Constructive Algebraic Hierarchy in Coq

Herman Geuvers, Randy Pollack, Freek Wiedijk, Jan Zwanenburg
2002 Journal of symbolic computation  
The algebraic hierarchy that is described here is both abstract and structured.  ...  The algebraic hierarchy is formalized in Coq by applying a combination of labelled record types and coercions.  ...  Furthermore, we want to thank Dan Synek, Henk Barendregt and Milad Niqui for valuable feedback and discussions.  ... 
doi:10.1006/jsco.2002.0552 fatcat:l5tzxkehqbbmvk64l5jiyfxkmy

Page 3537 of Mathematical Reviews Vol. , Issue 82h [page]

1982 Mathematical Reviews  
In this paper he solves the problem of finding a system of generators and of constructing a defining collection of relations in finite-valued data structure algebras.  ...  Relations in data structure algebras. II. Kibernetika ( Kiev) 1980, no. 1, i, 17-22, 149 ( Russian); translated as Cybernetics 16 (1980), no. 1, 18-24.  ... 

Page 4236 of Mathematical Reviews Vol. , Issue 81J [page]

1981 Mathematical Reviews  
The independence of the 81j:68031 time-varying record structure from the detailed way in which garbage collection and other operations are interleaved is shown to be a Church-Rosser type property of the  ...  The mathematics of record SIAM J. Comput. 9 (1980), no. 3, 441-469. The authors use algebraic graph theory to model sets of records (nodes) and pointers (arcs) in computer storage.  ... 

Page 1584 of Mathematical Reviews Vol. , Issue 84d [page]

1984 Mathematical Reviews  
Structures adapted to allow fast average search times and structures that allow partial match retrieval on records with d keys, d>1, are also considered.” Moroz, V.  ...  We explore the preservation of optimality under the operations of inserting a record into the file, deleting a specific record from the file, and deleting an arbitrary record from the file, showing that  ... 

Calculational Relation-Algebraic Proofs in Isabelle/Isar [chapter]

Wolfram Kahl
2004 Lecture Notes in Computer Science  
like Kleene algebras with tests [Koz97] and Kleene algebras with domain [DMS03].  ...  We propose a collection of theories in the proof assistant Isabelle/Isar that support calculational reasoning in and about heterogeneous relational algebras and Kleene algebras.  ...  Acknowledgements I am grateful to Millie Rhoss de Guzman and Hitoshi Furusawa for their comments on previous versions of this paper and many related discussions, and also to the anonymous reviewers for  ... 
doi:10.1007/978-3-540-24771-5_16 fatcat:smzaqpd5uzgw7fg5266chuohqu

Canonical structure in attribute based file organization

Eugene Wong, T. C. Chiang
1971 Communications of the ACM  
The structure is highly dependent on the way in which the file is to be used and is uniquely determined by the specification of the allowed queries.  ...  The desirable properties claimed for this structure are proved, and file maintenance questions are discussed.  ...  The aim of this paper is to make clear this dependence and to arrive at an optimal structure.  ... 
doi:10.1145/362663.362735 fatcat:mdjhjl6hlbgpvmitrljrr4vaou

Analytical Solution of Kolmogorov Equations for Four-Condition Homogenous, Symmetric and Ergodic System

Victor V. Kravets, Konstantin M. Bass, Vladimir V. Kravets, Larisa A. Tokar
2014 Open Journal of Applied Sciences  
Dependences of characteristic equation coefficients on intensity of failure and recovery flows are obtained.  ...  It is demonstrated that the coefficients of characteristic equation meet the demands of functional dependence matching proposed visible analytical solution of complete algebraic equation of fourth order  ...  The characteristic determinant ordering is expressed in structurally simple formulae for coefficients of dependence-bonded characteristic equation.  ... 
doi:10.4236/ojapps.2014.410048 fatcat:cfwt7fa3wnc5vir7xizmmn57je

Page 639 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
They also find sub- sets with ten and seven vectors for state-specific and probabilistic proofs, respectively (also records).  ...  If E is lattice ordered and vy is symmetric, then E is called a y-symmetric effect algebra. Various characterizations of y-symmetric effect algebras are given.  ... 
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